I have two variables which show a typical quantile relation
I would like to fit quantile regression models based on both logarithm and
polynomial of second order functions within quantreg.
Any help appreciated...
Cheers
Duccio

Herewith  the values:
------
var1    var2
0.96429    0.00138
1    0.02316
1.03145    0.09323
1.24088    0.77128
1.39869    0.86732
1.33728    0.63674
1.48299    0.96194
0.76    0.00001
0.77019    0.00003
0.96    0.00028
0.93491    0.00057
0.82432    0.00171
0.73077    0.00275
0.74648    0.00313
0.9697    0.00361
0.79245    0.00439
0.92994    0.00586
0.82143    0.00858
0.7377    0.00862
0.80795    0.01053
0.87075    0.01407
0.82993    0.01936
0.84507    0.01968
0.85185    0.03322
1.05063    0.03341
0.90123    0.03621
0.99415    0.0386
0.85714    0.03873
0.76259    0.04932
0.75188    0.05513
1.13122    0.06014
0.85333    0.06636
0.90411    0.0732
1.29778    0.07327
0.84211    0.08094
1.06024    0.08509
0.92208    0.08662
0.84354    0.09211
0.9359    0.09642
1.06286    0.10479
0.93333    0.10786
0.75    0.11703
0.79699    0.1214
0.88591    0.12347
0.80851    0.12404
0.80952    0.12424
0.83824    0.13017
0.95385    0.14673
1.02013    0.1513
0.8    0.1555
1.06667    0.15733
0.88732    0.16003
0.96154    0.18156
1.02247    0.18261
1.09877    0.18561
1.16564    0.18985
1.13333    0.19068
1.18239    0.20152
1.15663    0.21013
1.02941    0.22034
1.32381    0.22261
1.09459    0.23226
1.0068    0.23951
1.03614    0.26169
0.97222    0.26258
0.93878    0.28128
1.0137    0.28627
1.46087    0.28714
1.14451    0.28726
0.92913    0.28782
1.07595    0.30899
0.9635    0.34355
1.1677    0.36839
0.94595    0.38738
1.14118    0.39093
1.15429    0.40374
1.1625    0.41852
1.08235    0.42404
1.12941    0.43112
1.08176    0.44307
1.325    0.45221
1.38308    0.47239
1.0073    0.47427
1.17105    0.47728
1.13907    0.48632
1.34328    0.49487
1.20988    0.50787
1.36364    0.52367
1.21795    0.53399
1.23864    0.55555
1.23288    0.55839
1.28261    0.56652
1.35789    0.56932
1.22807    0.57798
1.2053    0.57992
1.18667    0.58031
1.1223    0.58048
1.10938    0.58197
1.29697    0.58868
1.22093    0.61025
1.21481    0.63087
1.58095    0.63506
1.34884    0.65639
1.2381    0.70642
1.51724    0.71612
1.34161    0.75399
1.45263    0.76035
1.28834    0.78978
1.53927    0.80492
1.35065    0.80679
1.38182    0.83345
1.3743    0.87256
1.6051    0.87435
1.3865    0.90878
1.44    0.94695
1.46405    0.95543
1.52941    0.96108
1.49686    0.98102
0.97436    0.00053
0.94972    0.03044
1.0838    0.04558
0.78322    0.04753
1.08791    0.06048
1.06832    0.06949
1.15294    0.13114
1.10067    0.18832
1.14124    0.23016
1.28814    0.25488
1.25316    0.25809
1.13333    0.26702
1.13772    0.41137
1.12346    0.43028
1.15385    0.47513
1.18621    0.48385
1.25301    0.52187
1.10959    0.56926
1.17391    0.57653
1.4    0.63667
1.22368    0.72883
1.41714    0.76351
1.33333    0.86687
1.33758    0.89052
1.45238    0.92793
1.39744    0.94344
1.48101    0.9775
0.7947    0.00049
0.94118    0.00078
0.90683    0.01507
0.78621    0.03443
1.05952    0.09995
0.92157    0.10748
0.98065    0.11945
1.05    0.15
1.09091    0.19752
0.86614    0.22126
1.21839    0.27116
1    0.28663
1.0375    0.31568
1.09554    0.362
1.09489    0.48028
1.22876    0.6107
1.27027    0.82497
1.47674    0.88388
1.36486    0.91599
1.5    0.9485
1.46429    0.96476
0.98429    0.00017
0.96    0.00132
1.1016    0.00164
1.03488    0.00259
1.13131    0.00676
1.12222    0.00857
1.17778    0.01879
0.84848    0.02734
1.04494    0.03203
0.99459    0.0334
1.06077    0.04496
0.99363    0.04525
0.9759    0.04738
0.84416    0.05265
1    0.06271
1.16384    0.06624
1.19255    0.10814
1.07865    0.11254
1.14839    0.11579
1.06587    0.11741
0.98795    0.15986
1.02564    0.16745
1.18232    0.24054
1.06475    0.26294
1.2028    0.33415
1.05263    0.33649
0.96203    0.35101
1.41899    0.36591
1.29032    0.38599
1.30337    0.39697
1.22581    0.40419
1.32231    0.41405
1.14286    0.41882
1.3121    0.48076
1.27684    0.49725
1.15152    0.50391
1.24103    0.52758
1.28485    0.53712
1.24706    0.55238
1.16312    0.589
1.24832    0.59592
1.19424    0.59958
1.23077    0.60055
1.15385    0.60596
1.17722    0.6227
1.32164    0.65736
1.28814    0.67897
1.35912    0.68161
1.21622    0.68561
1.2    0.69235
1.29323    0.69752
1.24242    0.72117
1.58779    0.7424
1.35938    0.75283
1.3038    0.76964
1.26389    0.78097
1.26619    0.78649
1.28467    0.78969
1.46821    0.81551
1.29496    0.82751
1.32886    0.82946
1.38346    0.86327
1.39623    0.88525
1.36585    0.89968
1.36986    0.91253
1.41844    0.92278
1.47297    0.92683
1.5894    0.93875
1.45205    0.95307
1.44    0.96991
1.51634    0.97627
1.11475    0.01352
0.95238    0.07429
0.94937    0.15717
1.32673    0.19765
1.1049    0.3566
1.14286    0.35769
1.175    0.38035
1.33981    0.38826
1.21101    0.39268
1.23871    0.41222
1.39623    0.43026
1.06542    0.45457
1.23636    0.46048
1.11538    0.50053
1.18121    0.50146
1.28205    0.5199
1.59116    0.53439
1.20721    0.53861
1.2125    0.56278
1.14286    0.57051
1.34545    0.57396
1.14286    0.57667
1.49254    0.59495
1.33945    0.61477
1.33913    0.63193
1.22835    0.64445
1.35593    0.64847
1.31579    0.65096
1.25373    0.65702
1.3007    0.65852
1.31579    0.6619
1.18797    0.66314
1.21212    0.67297
1.2381    0.67353
1.33333    0.67844
1.24691    0.67946
1.32174    0.69228
1.44715    0.70199
1.24138    0.70263
1.56075    0.70508
1.23741    0.70942
1.248    0.71058
1.41935    0.71489
1.45902    0.71796
1.3985    0.72005
1.35385    0.72072
1.18421    0.72409
1.23438    0.72432
1.45665    0.72434
1.31783    0.73215
1.48031    0.74742
1.37008    0.74794
1.45455    0.75231
1.57073    0.75479
1.32331    0.75782
1.34921    0.76381
1.37008    0.7654
1.27168    0.76891
1.39706    0.77234
1.33333    0.77396
1.46457    0.77448
1.26718    0.77722
1.30882    0.78328
1.44361    0.78838
1.33333    0.7899
1.39063    0.79478
1.31852    0.79676
1.62694    0.79723
1.27941    0.80713
1.29851    0.81276
1.43704    0.81624
1.32515    0.82265
1.30137    0.82293
1.62011    0.83007
1.41732    0.83096
1.46667    0.83266
1.41538    0.83821
1.33333    0.84023
1.33333    0.84138
1.41085    0.84395
1.41732    0.84445
1.40127    0.84476
1.41791    0.84816
1.3985    0.84903
1.59551    0.85226
1.42424    0.85227
1.47619    0.8553
1.46939    0.86723
1.37589    0.86943
1.51079    0.87004
1.51825    0.87195
1.3758    0.87532
1.36913    0.8759
1.39568    0.87671
1.38776    0.87762
1.47368    0.88003
1.36111    0.88012
1.43662    0.88274
1.41606    0.88282
1.5    0.88734
1.5    0.88944
1.40741    0.8911
1.5    0.89238
1.51773    0.89271
1.47518    0.89277
1.49275    0.89488
1.42029    0.90218
1.44681    0.9023
1.45324    0.90373
1.45695    0.90437
1.51479    0.90611
1.59777    0.90895
1.41429    0.91266
1.42197    0.91565
1.44286    0.91605
1.56906    0.91874
1.50968    0.91907
1.44828    0.92108
1.49189    0.92167
1.54717    0.92231
1.59524    0.92253
1.51678    0.92641
1.50355    0.92798
1.62195    0.92894
1.37037    0.93033
1.51389    0.93076
1.58889    0.93507
1.44681    0.93509
1.50685    0.93605
1.4375    0.93608
1.44056    0.93636
1.46309    0.93643
1.57895    0.93696
1.50588    0.93725
1.46479    0.93747
1.55556    0.93822
1.49275    0.93851
1.50838    0.93898
1.56213    0.93947
1.38562    0.93955
1.4965    0.93963
1.50336    0.94236
1.46405    0.9468
1.57576    0.94736
1.57055    0.94871
1.55705    0.94964
1.54054    0.94986
1.48966    0.95037
1.55422    0.95161
1.59006    0.95194
1.43243    0.952
1.47945    0.95236
1.57955    0.95298
1.46575    0.95502
1.44    0.95676
1.39869    0.95872
1.49686    0.95992
1.48299    0.96033
1.53247    0.96048
1.52    0.96081
1.45946    0.96093
1.50898    0.96104
1.62051    0.9615
1.44156    0.96264
1.48299    0.96337
1.5625    0.96343
1.52055    0.96494
1.55422    0.96533
1.46309    0.967
1.52    0.96777
1.50633    0.96783
1.50993    0.97162
1.50327    0.97442
1.51807    0.97464
1.43421    0.97542
1.47651    0.97671
1.52564    0.97791
1.52564    0.97873
1.5375    0.97932
1.50318    0.97948
1.51948    0.98
1.45223    0.98083
1.47561    0.98142
1.51634    0.98211
1.49701    0.98272
1.53293    0.9829
1.55556    0.98419
1.5375    0.98659
1.52632    0.98665
1.54545    0.98746
1.50968    0.98887
0.80292    0.02733
0.78788    0.05026
1.08387    0.25727
1.11236    0.28788
1.2093    0.32447
1.17333    0.35333
1.26486    0.35837
0.97297    0.36174
1.16763    0.37241
1.08609    0.4186
1.07285    0.50362
1.21333    0.51644
1.21379    0.62384
1.26241    0.62537
1.31818    0.65624
1.27007    0.71185
1.34161    0.71431
1.24286    0.71809
1.32308    0.73904
1.40157    0.76371
1.32919    0.7808
1.44118    0.78128
1.375    0.78208
1.40909    0.7947
1.29496    0.80487
1.38931    0.81096
1.42222    0.81254
1.29078    0.81377
1.31387    0.84942
1.3875    0.86737
1.40426    0.8828
1.49315    0.8853
1.36691    0.89381
1.41606    0.90245
1.48252    0.90975
1.58659    0.91133
1.5102    0.91485
1.48936    0.91897
1.41429    0.91995
1.3625    0.92154
1.56725    0.94172
1.51648    0.95473
1.42667    0.96679
1.46835    0.97723
1.54878    0.97943
1.4717    0.98295
1.02222    0.02021
1.41429    0.8753
0.76056    0.00006
0.79268    0.00057
0.78313    0.002
0.62626    0.00225
0.8    0.01268
0.89189    0.01448
0.88485    0.02624
1.00565    0.03471
1.0559    0.04432
0.83784    0.09914
1.04762    0.10191
0.73043    0.12486
1.23699    0.25224
1.39785    0.3089
1.025    0.31879
1.0719    0.33571
1.21212    0.38035
1.42105    0.40306
1.13158    0.41637
1.07692    0.51066
1.2716    0.52443
1.28302    0.55195
1.232    0.57827
1.16418    0.60219
1.30973    0.60664
1.22727    0.65079
1.43307    0.65682
1.38122    0.71209
1.40113    0.77652
1.48201    0.79789
1.44262    0.81144
1.35211    0.82607
1.36842    0.83288
1.30935    0.8429
1.35172    0.86687
1.55844    0.87823
1.64198    0.90079
1.35172    0.90976
1.59538    0.91276
1.44286    0.92195
1.3908    0.92303
1.57692    0.93374
1.57396    0.93416
1.47143    0.93515
1.43046    0.96609
1.46309    0.9666
1.47879    0.9669
1.52941    0.97006
1.55689    0.9797
1.53659    0.98209

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